Chapter 3: Induction & Pattern Recognition
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Induction is pattern recognition -- an inference based on limited observational or experimental data -- and pattern recognition is an addictively exhilarating acquired skill.
Of the two types of scientific inference, induction is far more pervasive and useful than deduction (Chapter 4). Induction usually infers some pattern among a set of observations and then attributes that pattern to an entire population. Almost all hypothesis formation is based consciously or subconsciously on induction.
Induction is pervasive because people seek order insatiably, yet they lack the opportunity of basing that search on observation of the entire population. Instead they make a few observations and generalize.
Induction is not just a description of observations; it is always a leap beyond the data -- a leap based on circumstantial evidence. The leap may be an inference that other observations would exhibit the same phenomena already seen in the study sample, or it may be some type of explanation or conceptual understanding of the observations; often it is both. Because induction is always a leap beyond the data, it can never be proved. If further observations are consistent with the induction, then they confirm, or lend substantiating support to, the induction. But the possibility always remains that as-yet-unexamined data might disprove the induction.
In symbols, we can think of confirmation of our inductive hypothesis A as: A⇒B, B, ∴A (i.e., A implies B; B is observed and therefore A must also be true or present). Such evidence may be inductively useful confirmation. The logic, however, is a deductive fallacy (known as affirming the consequent), because there may always be other factors that cause B. Although confirmation of an induction is incremental and inconclusive, the hypothesis can be disproved by a single experiment, via the deductive technique of modus tollens: A⇒B, -B, ∴-A (i.e., A implies B; B is not observed and therefore A must not be true or present).
Scientific induction requires that we make two unprovable assumptions, or postulates:
- representative sampling. Only if our samples are representative, or similar in behavior to the population as a whole, may we generalize from observations of these samples to the likely behavior of the entire population. In contrast, if our samples represent only a distinctive subset of the population, then our inductions cannot extend beyond this subset. This postulate is crucial, it is usually achieved easily by the scientist, and yet it is often violated with scientifically catastrophic results. As discussed more fully in the previous chapter, randomization and objective sampling are the paths to obtaining a representative sample; subjective sampling generates a biased sample.
- uniformity of nature. Strictly speaking, even if our sample is representative we cannot be certain that the unsampled remainder of the population exhibits the same behavior. However, we as -
